The answer is x = 4.154
Our expression is [tex] 14^{x-3} =21[/tex]
Logarith both sides of the expression:
[tex]log(14^{x-3}) =log(21)[/tex]
Since [tex]log( x^{a}) = a*log(x) [/tex], then [tex]log( 14^{x-3}) = (x-3)*log(14) [/tex]
Back to our expression:
[tex](x-3)*log(14)=log(21)[/tex]
[tex]x-3 = \frac{log(21)}{log(14)} [/tex]
[tex]x-3= \frac{1.322}{1.146} [/tex]
[tex]x -3 = 1.154 \\
x = 3 + 1.154 \\
x = 4.154[/tex]
